Winds measured by lidar from the Aeolus satellite are compared with winds measured by two ground-based radars - MARA in Antarctica (70.77 degrees S, 11.73 degrees E) and ES-RAD (67.88 degrees N, 21.10 degrees E) in Arctic Sweden - for the period 1 July-31 December 2019. Aeolus is a demonstrator mission to test whether winds measured by Doppler lidar from space can have sufficient accuracy to contribute to improved weather forecasting. A comprehensive programme of calibration and validation has been undertaken following the satellite launch in 2018, but, so far, direct comparison with independent measurements from the Arctic or Antarctic regions have not been made. The comparison covers heights from the low troposphere to just above the tropopause. Results for each radar site are presented separately for Rayleigh (clear) winds, Mie (cloudy) winds, sunlit ("summer") and non-sunlit ("winter") seasons, and ascending and descending satellite tracks. Horizontally projected line-of-sight (HLOS) winds from Aeolus, reprocessed using baseline 2B10, for passes within 100 km of the radar sites, are compared with HLOS winds calculated from 1 h averaged radar horizontal wind components. The agreement in most data subsets is very good, with no evidence of significant biases (<1ms(-1)). Possible biases are identified for two subsets (about -2ms(-1) for the Rayleigh winds for the descending passes at MARA and about 2ms(-1) for the Mie winds for the ascending passes at ESRAD, both in winter), but these are only marginally significant. A robust significant bias of about 7ms(-1) is found for the Mie winds for the ascending tracks at MARA in summer. There is also some evidence for increased random error (by about 1ms(-1) / for the Aeolus Mie winds at MARA in summer compared to winter. This might be related to the presence of sunlight scatter over the whole of Antarctica as Aeolus transits across it during summer.